The present invention pertains generally to devices which are useful for separating particles of a multi-species plasma according to their respective masses. More particularly, the present invention pertains to plasma mass filters which establish magnetic field configurations that direct charged particles along predetermined paths according to the mass of the specific particle. The present invention is particularly, but not exclusively, useful as a filter for a multi-species plasma that establishes a magnetic barrier which prevents selected particles from proceeding along a predetermined axial path through the filter.
It can be mathematically shown that the constants of motion for a charged particle (e.g. an ion) in an axially symmetric magnetic field are its angular momentum, P, and its kinetic energy, W. Mathematically, using a cylindrical coordinate system [r, xcex8, z], these constants of motion can be expressed as:
P=Mrvxcex8+e"psgr"
W=[M/2][vr2+vxcex82+vz2]
Where
xe2x80x9cMxe2x80x9d is the mass of the particle;
xe2x80x9crxe2x80x9d is the radial distance of the particle from the axis;
xe2x80x9cexe2x80x9d is the charge on a particle (ion);
xe2x80x9c"psgr"xe2x80x9d is the flux function of the magnetic field; and
xe2x80x9cvxe2x80x9d is velocity of the particle (vr, vxcex8, and vz are components of xe2x80x9cvxe2x80x9d).
Because the above expressions are general statements of the constants of motion, they are applicable to various situations and conditions. Specifically, for a configuration wherein two, otherwise substantially identical, axially symmetric magnetic fields are positioned co-axially, in an opposed back-to-back relationship, the above equations are applicable. For such a configuration, a null cusp is created in a plane perpendicular to the axis wherein the flux function, "psgr", is equal to zero. Stated differently, the flux function on opposite sides of the null will have opposite signs in the axial (z) direction. As a consequence of this condition, a charged particle is able to cross the cusp only if it has the necessary momentum and energy to do so.
Because both the momentum and the energy of a particle are functions of the mass of the particle, and due to the fact there will be a conservation of the particle""s momentum and energy in a system, an expression can be mathematically derived which will relate the mass of the particle to its ability to cross through a null cusp. Here, of course, we are considering the null cusp as described above. Specifically, in this context, for a given energy, W, and for a given magnetic field magnitude, B, a cut-off mass, Mc, can be identified such that particles with a mass M2 greater than Mc (M2 greater than Mc) will cross the null cusp, while particles with a mass M1 less than Mc (M1 less than Mc) will not cross the null cusp. The expression for this Mc is:
Mc=e2B2r2/2W.
In another aspect of particle physics, it is well known that a charged particle in a magnetic field will have a cyclotron frequency, f, which can be mathematically expressed as: f=Be/2xcfx80M. Further, it is known that all charged particles are subject to cyclotron resonance heating wherein a charged particle (electrons or ions) will selectively absorb energy by resonance coupling. Importantly, this resonance coupling is a function of the mass of the particle. Therefore, all ions of a predetermined mass in a multi-species plasma can be selectively heated by resonance coupling, while ions of other masses are not so heated.
In the environment of the opposed axi-symmetric magnetic fields described above, it is to be appreciated that a charged particle (ion) can have either of two types of obits. In a so-called type-1 orbit, the projection of the orbit onto a plane perpendicular to the magnetic field does not encircle the origin. In this case (type-1 orbit) the angular momentum, P, and the magnetic flux function, "psgr", have the same sign (i.e. P"psgr" greater than 0). Also, Mrvxcex8is of opposite sign but is less than the flux function "psgr"(i.e. |P| less than |"psgr"|). On the other hand, in a type-2 orbit the projection of the orbit onto a plane perpendicular to the magnetic field encircles the origin. In this case (type-2 orbit) the angular momentum, P, and the magnetic flux function, "psgr", have opposite signs (i.e. P"psgr" less than 0). In this case, Mrvxcex8is greater in magnitude than the flux function "psgr" and is of opposite sign (i.e. |P| less than |"psgr"|). It can be mathematically shown that the switch between a type-1 orbit and a type-2 orbit involves a large change in the angular momentum P. A consequence of this is that the orbit of a particle must change from type-1 to type-2, or vice versa, as a particle crosses through a null cusp.
It happens that the concepts discussed above regarding axi-symmetric magnetic fields, cyclotron resonance heating, and different type orbits, are not mutually exclusive. Specifically, for purposes of separating the charged particles of a multi-species plasma from each other according to their respective masses, the concepts just discussed can be used interrelatedly. In one application, the energies (W) of charged particles in a multi-species plasma can be used to establish a cut-off mass, Mc, where M1 less than Mc less than M2 with Mc=e2B2r2/2W, so that lower mass ions, M1, will not cross the cusp, but the higher ions, M2, will. In another application, selected particles of mass Ms, in a multi-species plasma, can have their energy and momentum raised by cyclotron resonance heating so that only particles having the selected mass, Ms, will cross the cusp. In this second application, the expression for the cut-off mass is normalized such that with Mc/Ms=1=e2B2rs2/2WsMs.
In light of the above, it is an object of the present invention to provide a cusp filter which will selectively heat ions of a particular mass in a multi-species plasma so that the selected particles can be separated from other particles in the plasma. Another object of the present invention is to provide a cusp filter wherein particles selected for separation from other particles have their energy and momentum elevated above other particles in a multi-species plasma by cyclotron resonance heating. Yet another object of the present invention is to provide a cusp filter which establishes a magnetic field configuration wherein a cut-off mass, Mc, can be determined so that particles having masses greater than Mc will be influenced differently than particles having masses less than Mc to thereby separate the particles of different mass from each other. Still another object of the present invention is to provide a cusp filter which is relatively easy to manufacture, simple to use, and comparatively cost effective.
A cusp filter in accordance with the present invention includes components for generating a magnetic null cusp that is located between opposed, axi-symmetric, back-to-back magnetic fields. Both of the back-to back magnetic fields in this case have equal magnitudes that are substantially equal to xe2x80x9cB.xe2x80x9d Their respective magnetic field lines, however, are oriented in opposite directions along their mutual axis. With these orientations, the two magnetic fields establish a magnetic null cusp between them, in a plane that is oriented substantially perpendicular to the axis. As contemplated by the present invention, the opposed back-to-back magnetic fields are each generated in the chamber of a container, by a respective plurality of magnetic coils which are mounted on the container.
The cusp filter of the present invention also includes an injector. In addition to generating a multi-species plasma, the purpose of this injector is to direct both relatively low mass ions (M1) and relatively high mass ions (M2) in the multi-species plasma along the axis in the chamber toward the null cusp. As contemplated for the present invention, the separation of ions at the null cusp according to their respective masses can be initiated in either of two ways.
For one embodiment of the present invention, differences in either the energy or the momenta of ions in the multi-species are exploited to separate ions of mass (M1) from ions of mass (M2). More specifically, due to the relatively low energy, or momentum, of the low mass ions (M1) they are prevented from crossing the null cusp. Instead, they are diverted away from the axis by the null cusp for subsequent collection. On the other hand, the relatively high energy, or momentum, of the high mass ions (M2) will allow these ions to cross the null cusp and proceed along the axis through the filter chamber for subsequent collection. For this particular embodiment of the present invention, the magnitude, B, of the magnetic fields can be selected to identify a cut-off mass, Mc, such that M1 less than Mc less than M2. The expression Mc=e2B2r2/2W can then be applied where xe2x80x9cexe2x80x9d is the ion charge, xe2x80x9crxe2x80x9d is the radial distance of an ion (charged particle) from the axis in the first magnetic. field, and W is the kinetic energy of the ion. In accordance with the expression for Mc, it will appreciated that the cusp filter can achieve its intended result if either the energy of the ions (M1) is substantially equal to the energy of the ions (M2), or the ions (M1) and (M2) are directed toward the null cusp at a substantially common axial velocity.
In an alternate embodiment of the present invention, ions of a selected mass, Ms, can be specifically targeted for separation from other ions in a multi-species plasma. Importantly, this can be accomplished regardless whether the selected ions are of comparably higher or lower mass. To do this, the ions of selected mass, Ms, are heated by cyclotron resonance. The energy of the resonance heated ions is thereby raised substantially above the energies of the other, non-selected ions in the multi-species plasma. As contemplated by the present invention, cyclotron resonance is accomplished using a cyclotron harmonics accelerator, such as a quadrant antenna. For this purpose, the quadrant antenna is operated at twice the resonant cyclotron frequency of the selected ions (2f). Consequently, due to the higher energies of the selected ions, when the multi-species plasma is directed toward the null cusp, the resonance heated ions will cross the cusp and continue their transit through the filter. The other ions, however, having lower energy, will be diverted from the filter by the null cusp and they will thereby be separated from the selected ions.
For either embodiment of the present invention, the cusp filter of the present invention will include a vacuum pump which is connected to the container. Specifically, the vacuum pump is used to maintain the multi-species plasma below a collisional density in the chamber. For purposes of the present invention, this collisional density is defined as a density wherein an ion can cross the null cusp before suffering a collision with another ion. Hence, the collisional density is achieved in a condition wherein the ratio of the collision frequency of an ion to its cyclotron frequency is less than the ratio of the distance of the ion from the axis, r, to the axial distance between the ion and the null cusp.
Several additional aspects of the cusp filter will apply regardless of its particular embodiment. For one, the cusp filter will include a radial collector that is mounted on the container and oriented substantially in the plane of the null cusp. As so positioned the radial collector is used for collecting ions as they are diverted away from the axis. Additionally the cusp filter can include an axial collector that is positioned substantially on the axis for collecting the ions as they proceed along the axis through the filter. In another aspect, the cusp filter can include a plurality of electrodes positioned on the container to bias the magnetic field immediately downstream from the injector to produce a radial electric field for uniformly increasing the energies of the ions in the multi-species plasma to reduce the sensitivity of Mc to r. Finally, it is also possible for the cusp filter to incorporate an axi-symmetric third magnetic field which is coaxial with the first pair of back-to-back magnetic fields. If this is done, the third magnetic field will have a magnitude substantially equal to B, and it will have magnetic field lines that are oriented in opposition to the magnetic field lines of the middle magnetic field. With this configuration, a second null cusp will be established to divert ions away from the axis, in a manner as described above, to enhance the separation of ions in the multi-species plasma.